Analisis Regresi Linier Berganda adalah model regresi linier dengan melibatkan lebih dari satu variabel bebas atau predictor.
library(MASS)## Warning: package 'MASS' was built under R version 3.5.3library(car)## Loading required package: carDataMembaca data dari file format csv
carmodel <- read.csv("Carprice_Dataset.csv")Melihat 6 baris data dari atas
head(carmodel)## car_ID symboling CarName fueltype aspiration doornumber
## 1 1 3 alfa-romero giulia gas std two
## 2 2 3 alfa-romero stelvio gas std two
## 3 3 1 alfa-romero Quadrifoglio gas std two
## 4 4 2 audi 100 ls gas std four
## 5 5 2 audi 100ls gas std four
## 6 6 2 audi fox gas std two
## carbody drivewheel enginelocation wheelbase carlength carwidth
## 1 convertible rwd front 88.6 168.8 64.1
## 2 convertible rwd front 88.6 168.8 64.1
## 3 hatchback rwd front 94.5 171.2 65.5
## 4 sedan fwd front 99.8 176.6 66.2
## 5 sedan 4wd front 99.4 176.6 66.4
## 6 sedan fwd front 99.8 177.3 66.3
## carheight curbweight enginetype cylindernumber enginesize fuelsystem
## 1 48.8 2548 dohc four 130 mpfi
## 2 48.8 2548 dohc four 130 mpfi
## 3 52.4 2823 ohcv six 152 mpfi
## 4 54.3 2337 ohc four 109 mpfi
## 5 54.3 2824 ohc five 136 mpfi
## 6 53.1 2507 ohc five 136 mpfi
## boreratio stroke compressionratio horsepower peakrpm citympg highwaympg
## 1 3.47 2.68 9.0 111 5000 21 27
## 2 3.47 2.68 9.0 111 5000 21 27
## 3 2.68 3.47 9.0 154 5000 19 26
## 4 3.19 3.40 10.0 102 5500 24 30
## 5 3.19 3.40 8.0 115 5500 18 22
## 6 3.19 3.40 8.5 110 5500 19 25
## price
## 1 13495
## 2 16500
## 3 16500
## 4 13950
## 5 17450
## 6 15250Struktur Data
str(carmodel)## 'data.frame': 205 obs. of 26 variables:
## $ car_ID : int 1 2 3 4 5 6 7 8 9 10 ...
## $ symboling : int 3 3 1 2 2 2 1 1 1 0 ...
## $ CarName : Factor w/ 147 levels "alfa-romero giulia",..: 1 3 2 4 5 9 5 7 6 8 ...
## $ fueltype : Factor w/ 2 levels "diesel","gas": 2 2 2 2 2 2 2 2 2 2 ...
## $ aspiration : Factor w/ 2 levels "std","turbo": 1 1 1 1 1 1 1 1 2 2 ...
## $ doornumber : Factor w/ 2 levels "four","two": 2 2 2 1 1 2 1 1 1 2 ...
## $ carbody : Factor w/ 5 levels "convertible",..: 1 1 3 4 4 4 4 5 4 3 ...
## $ drivewheel : Factor w/ 3 levels "4wd","fwd","rwd": 3 3 3 2 1 2 2 2 2 1 ...
## $ enginelocation : Factor w/ 2 levels "front","rear": 1 1 1 1 1 1 1 1 1 1 ...
## $ wheelbase : num 88.6 88.6 94.5 99.8 99.4 ...
## $ carlength : num 169 169 171 177 177 ...
## $ carwidth : num 64.1 64.1 65.5 66.2 66.4 66.3 71.4 71.4 71.4 67.9 ...
## $ carheight : num 48.8 48.8 52.4 54.3 54.3 53.1 55.7 55.7 55.9 52 ...
## $ curbweight : int 2548 2548 2823 2337 2824 2507 2844 2954 3086 3053 ...
## $ enginetype : Factor w/ 7 levels "dohc","dohcv",..: 1 1 6 4 4 4 4 4 4 4 ...
## $ cylindernumber : Factor w/ 7 levels "eight","five",..: 3 3 4 3 2 2 2 2 2 2 ...
## $ enginesize : int 130 130 152 109 136 136 136 136 131 131 ...
## $ fuelsystem : Factor w/ 8 levels "1bbl","2bbl",..: 6 6 6 6 6 6 6 6 6 6 ...
## $ boreratio : num 3.47 3.47 2.68 3.19 3.19 3.19 3.19 3.19 3.13 3.13 ...
## $ stroke : num 2.68 2.68 3.47 3.4 3.4 3.4 3.4 3.4 3.4 3.4 ...
## $ compressionratio: num 9 9 9 10 8 8.5 8.5 8.5 8.3 7 ...
## $ horsepower : int 111 111 154 102 115 110 110 110 140 160 ...
## $ peakrpm : int 5000 5000 5000 5500 5500 5500 5500 5500 5500 5500 ...
## $ citympg : int 21 21 19 24 18 19 19 19 17 16 ...
## $ highwaympg : int 27 27 26 30 22 25 25 25 20 22 ...
## $ price : num 13495 16500 16500 13950 17450 ...Membersihkan data dari \ .* pada variabel Carname
carmodel$companyname <- gsub("\\ .*", "", carmodel$CarName)Melihat isi variabel dari data carmodel
unique(carmodel$companyname)## [1] "alfa-romero" "audi" "bmw" "chevrolet" "dodge"
## [6] "honda" "isuzu" "jaguar" "maxda" "mazda"
## [11] "buick" "mercury" "mitsubishi" "Nissan" "nissan"
## [16] "peugeot" "plymouth" "porsche" "porcshce" "renault"
## [21] "saab" "subaru" "toyota" "toyouta" "vokswagen"
## [26] "volkswagen" "vw" "volvo"Mengganti nama-nama mobil dari variabel companyname
#vokswagen => volkswagen
carmodel$companyname <- gsub("vokswagen","volkswagen",carmodel$companyname)
#maxda=>mazda
carmodel$companyname <- gsub("maxda","mazda",carmodel$companyname)
#Nissan=>nissan
carmodel$companyname <- gsub("Nissan","nissan",carmodel$companyname)
#porcshce=>porsche
carmodel$companyname <- gsub("porcshce","porsche",carmodel$companyname)
#vw=>volkswagen
carmodel$companyname <- gsub("vw","volkswagen",carmodel$companyname)
#toyouta=>toyota
carmodel$companyname <- gsub("toyouta","toyota",carmodel$companyname)Melihat isi data dari variabel companyname
unique(carmodel$companyname)## [1] "alfa-romero" "audi" "bmw" "chevrolet" "dodge"
## [6] "honda" "isuzu" "jaguar" "mazda" "buick"
## [11] "mercury" "mitsubishi" "nissan" "peugeot" "plymouth"
## [16] "porsche" "renault" "saab" "subaru" "toyota"
## [21] "volkswagen" "volvo"melihat hasil NA
sum(is.na(carmodel))## [1] 0Menentukan elemen yang mengalami duplikat
sum(duplicated(carmodel)) ## [1] 0Melihat isi data dari variabel symboling,fueltype,aspiration,doornumber,carbody,drivewheel
unique(carmodel$symboling)## [1] 3 1 2 0 -1 -2unique(carmodel$fueltype)## [1] gas diesel
## Levels: diesel gasunique(carmodel$aspiration)## [1] std turbo
## Levels: std turbounique(carmodel$doornumber)## [1] two four
## Levels: four twounique(carmodel$carbody)## [1] convertible hatchback sedan wagon hardtop
## Levels: convertible hardtop hatchback sedan wagonunique(carmodel$drivewheel)## [1] rwd fwd 4wd
## Levels: 4wd fwd rwdMembuat menjadi huruf kapital
carmodel$companyname <- toupper(carmodel$companyname)Membuat data pada kolom menjadi bertipe factor
carmodel$symboling <- as.factor(carmodel$symboling)
carmodel$CarName <- as.factor(carmodel$CarName)
carmodel$carbody <- as.factor(carmodel$carbody)
carmodel$drivewheel <- as.factor(carmodel$drivewheel)
carmodel$enginelocation <- as.factor(carmodel$enginelocation)
carmodel$cylindernumber <- as.factor(carmodel$cylindernumber)
carmodel$doornumber <- as.factor(carmodel$doornumber)
carmodel$fuelsystem <- as.factor(carmodel$fuelsystem)
carmodel$aspiration <- as.factor(carmodel$aspiration)
carmodel$enginetype <- as.factor(carmodel$enginetype)
carmodel$fueltype <- as.factor(carmodel$fueltype)Struktur dari data carmodel
str(carmodel)## 'data.frame': 205 obs. of 27 variables:
## $ car_ID : int 1 2 3 4 5 6 7 8 9 10 ...
## $ symboling : Factor w/ 6 levels "-2","-1","0",..: 6 6 4 5 5 5 4 4 4 3 ...
## $ CarName : Factor w/ 147 levels "alfa-romero giulia",..: 1 3 2 4 5 9 5 7 6 8 ...
## $ fueltype : Factor w/ 2 levels "diesel","gas": 2 2 2 2 2 2 2 2 2 2 ...
## $ aspiration : Factor w/ 2 levels "std","turbo": 1 1 1 1 1 1 1 1 2 2 ...
## $ doornumber : Factor w/ 2 levels "four","two": 2 2 2 1 1 2 1 1 1 2 ...
## $ carbody : Factor w/ 5 levels "convertible",..: 1 1 3 4 4 4 4 5 4 3 ...
## $ drivewheel : Factor w/ 3 levels "4wd","fwd","rwd": 3 3 3 2 1 2 2 2 2 1 ...
## $ enginelocation : Factor w/ 2 levels "front","rear": 1 1 1 1 1 1 1 1 1 1 ...
## $ wheelbase : num 88.6 88.6 94.5 99.8 99.4 ...
## $ carlength : num 169 169 171 177 177 ...
## $ carwidth : num 64.1 64.1 65.5 66.2 66.4 66.3 71.4 71.4 71.4 67.9 ...
## $ carheight : num 48.8 48.8 52.4 54.3 54.3 53.1 55.7 55.7 55.9 52 ...
## $ curbweight : int 2548 2548 2823 2337 2824 2507 2844 2954 3086 3053 ...
## $ enginetype : Factor w/ 7 levels "dohc","dohcv",..: 1 1 6 4 4 4 4 4 4 4 ...
## $ cylindernumber : Factor w/ 7 levels "eight","five",..: 3 3 4 3 2 2 2 2 2 2 ...
## $ enginesize : int 130 130 152 109 136 136 136 136 131 131 ...
## $ fuelsystem : Factor w/ 8 levels "1bbl","2bbl",..: 6 6 6 6 6 6 6 6 6 6 ...
## $ boreratio : num 3.47 3.47 2.68 3.19 3.19 3.19 3.19 3.19 3.13 3.13 ...
## $ stroke : num 2.68 2.68 3.47 3.4 3.4 3.4 3.4 3.4 3.4 3.4 ...
## $ compressionratio: num 9 9 9 10 8 8.5 8.5 8.5 8.3 7 ...
## $ horsepower : int 111 111 154 102 115 110 110 110 140 160 ...
## $ peakrpm : int 5000 5000 5000 5500 5500 5500 5500 5500 5500 5500 ...
## $ citympg : int 21 21 19 24 18 19 19 19 17 16 ...
## $ highwaympg : int 27 27 26 30 22 25 25 25 20 22 ...
## $ price : num 13495 16500 16500 13950 17450 ...
## $ companyname : chr "ALFA-ROMERO" "ALFA-ROMERO" "ALFA-ROMERO" "AUDI" ...Mengubah data factor menjadi data tipe numeric
#Mengubah data factor menjadi data tipe numeric
levels(carmodel$enginelocation) <- c(1,0)
carmodel$enginelocation <- as.numeric(levels(carmodel$enginelocation))[carmodel$enginelocation]
#Mengubah data factor menjadi data tipe numeric
levels(carmodel$doornumber) <- c(1,0)
carmodel$doornumber <- as.numeric(levels(carmodel$doornumber))[carmodel$doornumber]
#Mengubah data factor menjadi data tipe numeric
levels(carmodel$fueltype) <- c(1,0)
carmodel$fueltype <- as.numeric(levels(carmodel$fueltype))[carmodel$fueltype]
#Mengubah data factor menjadi data tipe numeric
levels(carmodel$aspiration) <-c(1,0)
carmodel$aspiration <- as.numeric(levels(carmodel$aspiration))[carmodel$aspiration]Membuat data factor menjadi data biner
#Membuat data factor menjadi data biner
dummy_drivewheel <- as.data.frame(model.matrix(~drivewheel,data = carmodel))
dummy_drivewheel <- dummy_drivewheel[,-1]
carmodel <- cbind(carmodel[,-which(colnames(carmodel)=='drivewheel')],dummy_drivewheel)
#Membuat data factor menjadi data biner
dummy_carbody <- as.data.frame(model.matrix(~carbody,data = carmodel))
dummy_carbody <- dummy_carbody[,-1]
carmodel <- cbind(carmodel[,-which(colnames(carmodel)=='carbody')],dummy_carbody)
#Membuat data factor menjadi data biner
dummy_enginetype <- as.data.frame(model.matrix(~enginetype,data = carmodel))
dummy_enginetype <- dummy_enginetype[,-1]
carmodel <- cbind(carmodel[,-which(colnames(carmodel)=='enginetype')],dummy_enginetype)
#Membuat data factor menjadi data biner
dummy_cylindernumber <- as.data.frame(model.matrix(~cylindernumber,data = carmodel))
dummy_cylindernumber <- dummy_cylindernumber[,-1]
carmodel <- cbind(carmodel[,-which(colnames(carmodel)=='cylindernumber')],dummy_cylindernumber)
#Membuat data factor menjadi data biner
dummy_fuelsystem <- as.data.frame(model.matrix(~fuelsystem,data = carmodel))
dummy_fuelsystem <- dummy_fuelsystem[,-1]
carmodel <- cbind(carmodel[,-which(colnames(carmodel)=='fuelsystem')],dummy_fuelsystem)
#Membuat data factor menjadi data biner
dummy_companyname <- as.data.frame(model.matrix(~companyname,data = carmodel))
dummy_companyname <- dummy_companyname[,-1]
carmodel <- cbind(carmodel[,-which(colnames(carmodel)=='companyname')],dummy_companyname)
#Membuat data factor menjadi data biner
dummy_symboling <- as.data.frame(model.matrix(~symboling,data = carmodel))
dummy_symboling <- dummy_symboling[,-1]
carmodel <- cbind(carmodel[,-which(colnames(carmodel)=='symboling')],dummy_symboling)Menghilangkan variabel CarName
carmodel <- carmodel[,-which(colnames(carmodel)=='CarName')]
str(carmodel)## 'data.frame': 205 obs. of 70 variables:
## $ car_ID : int 1 2 3 4 5 6 7 8 9 10 ...
## $ fueltype : num 0 0 0 0 0 0 0 0 0 0 ...
## $ aspiration : num 1 1 1 1 1 1 1 1 0 0 ...
## $ doornumber : num 0 0 0 1 1 0 1 1 1 0 ...
## $ enginelocation : num 1 1 1 1 1 1 1 1 1 1 ...
## $ wheelbase : num 88.6 88.6 94.5 99.8 99.4 ...
## $ carlength : num 169 169 171 177 177 ...
## $ carwidth : num 64.1 64.1 65.5 66.2 66.4 66.3 71.4 71.4 71.4 67.9 ...
## $ carheight : num 48.8 48.8 52.4 54.3 54.3 53.1 55.7 55.7 55.9 52 ...
## $ curbweight : int 2548 2548 2823 2337 2824 2507 2844 2954 3086 3053 ...
## $ enginesize : int 130 130 152 109 136 136 136 136 131 131 ...
## $ boreratio : num 3.47 3.47 2.68 3.19 3.19 3.19 3.19 3.19 3.13 3.13 ...
## $ stroke : num 2.68 2.68 3.47 3.4 3.4 3.4 3.4 3.4 3.4 3.4 ...
## $ compressionratio : num 9 9 9 10 8 8.5 8.5 8.5 8.3 7 ...
## $ horsepower : int 111 111 154 102 115 110 110 110 140 160 ...
## $ peakrpm : int 5000 5000 5000 5500 5500 5500 5500 5500 5500 5500 ...
## $ citympg : int 21 21 19 24 18 19 19 19 17 16 ...
## $ highwaympg : int 27 27 26 30 22 25 25 25 20 22 ...
## $ price : num 13495 16500 16500 13950 17450 ...
## $ drivewheelfwd : num 0 0 0 1 0 1 1 1 1 0 ...
## $ drivewheelrwd : num 1 1 1 0 0 0 0 0 0 0 ...
## $ carbodyhardtop : num 0 0 0 0 0 0 0 0 0 0 ...
## $ carbodyhatchback : num 0 0 1 0 0 0 0 0 0 1 ...
## $ carbodysedan : num 0 0 0 1 1 1 1 0 1 0 ...
## $ carbodywagon : num 0 0 0 0 0 0 0 1 0 0 ...
## $ enginetypedohcv : num 0 0 0 0 0 0 0 0 0 0 ...
## $ enginetypel : num 0 0 0 0 0 0 0 0 0 0 ...
## $ enginetypeohc : num 0 0 0 1 1 1 1 1 1 1 ...
## $ enginetypeohcf : num 0 0 0 0 0 0 0 0 0 0 ...
## $ enginetypeohcv : num 0 0 1 0 0 0 0 0 0 0 ...
## $ enginetyperotor : num 0 0 0 0 0 0 0 0 0 0 ...
## $ cylindernumberfive : num 0 0 0 0 1 1 1 1 1 1 ...
## $ cylindernumberfour : num 1 1 0 1 0 0 0 0 0 0 ...
## $ cylindernumbersix : num 0 0 1 0 0 0 0 0 0 0 ...
## $ cylindernumberthree : num 0 0 0 0 0 0 0 0 0 0 ...
## $ cylindernumbertwelve : num 0 0 0 0 0 0 0 0 0 0 ...
## $ cylindernumbertwo : num 0 0 0 0 0 0 0 0 0 0 ...
## $ fuelsystem2bbl : num 0 0 0 0 0 0 0 0 0 0 ...
## $ fuelsystem4bbl : num 0 0 0 0 0 0 0 0 0 0 ...
## $ fuelsystemidi : num 0 0 0 0 0 0 0 0 0 0 ...
## $ fuelsystemmfi : num 0 0 0 0 0 0 0 0 0 0 ...
## $ fuelsystemmpfi : num 1 1 1 1 1 1 1 1 1 1 ...
## $ fuelsystemspdi : num 0 0 0 0 0 0 0 0 0 0 ...
## $ fuelsystemspfi : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameAUDI : num 0 0 0 1 1 1 1 1 1 1 ...
## $ companynameBMW : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameBUICK : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameCHEVROLET : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameDODGE : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameHONDA : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameISUZU : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameJAGUAR : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameMAZDA : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameMERCURY : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameMITSUBISHI: num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameNISSAN : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynamePEUGEOT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynamePLYMOUTH : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynamePORSCHE : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameRENAULT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameSAAB : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameSUBARU : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameTOYOTA : num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameVOLKSWAGEN: num 0 0 0 0 0 0 0 0 0 0 ...
## $ companynameVOLVO : num 0 0 0 0 0 0 0 0 0 0 ...
## $ symboling-1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ symboling0 : num 0 0 0 0 0 0 0 0 0 1 ...
## $ symboling1 : num 0 0 1 0 0 0 1 1 1 0 ...
## $ symboling2 : num 0 0 0 1 1 1 0 0 0 0 ...
## $ symboling3 : num 1 1 0 0 0 0 0 0 0 0 ...Menghitung jumlah nilai yang kosong
sum(is.na(carmodel))## [1] 0Mengatur data training dan testing
set.seed(12345)
trainindices <- sample(1:nrow(carmodel),0.7*nrow(carmodel))
train = carmodel[trainindices,]
test = carmodel[-trainindices,]Mencoba membuat model untuk melihat variabel yang berpengaruh
model_1 <- lm(price~.,data = train)
summary(model_1)##
## Call:
## lm(formula = price ~ ., data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2512.1 -673.1 0.0 653.2 3035.6
##
## Coefficients: (5 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.188e+04 2.071e+04 -1.057 0.293903
## car_ID 1.569e+02 6.634e+01 2.364 0.020547 *
## fueltype 1.323e+04 7.902e+03 1.674 0.098197 .
## aspiration -2.213e+03 1.264e+03 -1.751 0.083908 .
## doornumber 2.048e+02 6.150e+02 0.333 0.740059
## enginelocation -3.613e+04 1.073e+04 -3.368 0.001179 **
## wheelbase -3.203e+01 1.333e+02 -0.240 0.810767
## carlength 1.161e+01 6.664e+01 0.174 0.862153
## carwidth 7.942e+02 2.710e+02 2.930 0.004442 **
## carheight 2.455e+02 1.778e+02 1.380 0.171420
## curbweight 4.665e+00 1.772e+00 2.632 0.010215 *
## enginesize 7.670e+01 3.110e+01 2.466 0.015858 *
## boreratio -2.709e+03 1.970e+03 -1.375 0.173061
## stroke -1.076e+03 1.143e+03 -0.941 0.349410
## compressionratio -1.026e+03 5.817e+02 -1.763 0.081751 .
## horsepower -1.407e+01 3.029e+01 -0.465 0.643509
## peakrpm 1.756e+00 8.101e-01 2.167 0.033278 *
## citympg 1.371e+02 1.760e+02 0.779 0.438462
## highwaympg 4.996e+01 1.678e+02 0.298 0.766758
## drivewheelfwd 6.152e+02 9.472e+02 0.650 0.517883
## drivewheelrwd -3.218e+02 1.333e+03 -0.241 0.809851
## carbodyhardtop -2.439e+03 1.155e+03 -2.112 0.037899 *
## carbodyhatchback -2.773e+03 1.101e+03 -2.519 0.013800 *
## carbodysedan -3.644e+03 1.244e+03 -2.930 0.004444 **
## carbodywagon -4.512e+03 1.364e+03 -3.309 0.001417 **
## enginetypedohcv -3.529e+03 5.088e+03 -0.694 0.490020
## enginetypel -2.297e+04 7.896e+03 -2.910 0.004714 **
## enginetypeohc -1.636e+02 1.424e+03 -0.115 0.908826
## enginetypeohcf -2.701e+04 1.033e+04 -2.614 0.010722 *
## enginetypeohcv -2.547e+03 1.340e+03 -1.901 0.060944 .
## enginetyperotor 1.016e+04 5.377e+03 1.889 0.062632 .
## cylindernumberfive -4.201e+03 3.409e+03 -1.232 0.221474
## cylindernumberfour -2.977e+03 4.205e+03 -0.708 0.481063
## cylindernumbersix -2.560e+03 3.378e+03 -0.758 0.450904
## cylindernumberthree 2.251e+04 8.897e+03 2.530 0.013406 *
## cylindernumbertwelve 4.266e+02 5.535e+03 0.077 0.938761
## cylindernumbertwo NA NA NA NA
## fuelsystem2bbl 2.300e+03 1.505e+03 1.528 0.130524
## fuelsystem4bbl -2.155e+02 2.460e+03 -0.088 0.930408
## fuelsystemidi NA NA NA NA
## fuelsystemmfi 9.559e+02 2.655e+03 0.360 0.719765
## fuelsystemmpfi 1.749e+03 1.628e+03 1.074 0.285946
## fuelsystemspdi 1.058e+03 1.870e+03 0.566 0.573245
## fuelsystemspfi NA NA NA NA
## companynameAUDI -4.301e+03 2.805e+03 -1.533 0.129222
## companynameBMW 3.169e+03 2.663e+03 1.190 0.237616
## companynameBUICK -5.803e+03 4.928e+03 -1.178 0.242533
## companynameCHEVROLET -8.571e+03 3.341e+03 -2.566 0.012220 *
## companynameDODGE -1.036e+04 2.913e+03 -3.554 0.000647 ***
## companynameHONDA -9.615e+03 3.684e+03 -2.610 0.010851 *
## companynameISUZU -1.024e+04 4.195e+03 -2.442 0.016879 *
## companynameJAGUAR -4.234e+03 3.791e+03 -1.117 0.267500
## companynameMAZDA -1.563e+04 4.831e+03 -3.235 0.001783 **
## companynameMERCURY -1.590e+04 5.885e+03 -2.701 0.008478 **
## companynameMITSUBISHI -1.917e+04 6.176e+03 -3.104 0.002662 **
## companynameNISSAN -2.013e+04 7.223e+03 -2.787 0.006687 **
## companynamePEUGEOT NA NA NA NA
## companynamePLYMOUTH -2.481e+04 8.678e+03 -2.859 0.005449 **
## companynamePORSCHE -1.347e+04 8.784e+03 -1.533 0.129200
## companynameRENAULT -2.650e+04 9.070e+03 -2.922 0.004549 **
## companynameSAAB -2.419e+04 9.471e+03 -2.554 0.012587 *
## companynameSUBARU NA NA NA NA
## companynameTOYOTA -3.040e+04 1.137e+04 -2.674 0.009117 **
## companynameVOLKSWAGEN -3.382e+04 1.307e+04 -2.588 0.011523 *
## companynameVOLVO -3.038e+04 1.291e+04 -2.353 0.021169 *
## `symboling-1` 1.965e+03 1.424e+03 1.380 0.171596
## symboling0 3.400e+03 1.762e+03 1.929 0.057326 .
## symboling1 4.117e+03 1.811e+03 2.273 0.025756 *
## symboling2 3.438e+03 1.826e+03 1.883 0.063409 .
## symboling3 2.571e+03 1.908e+03 1.347 0.181725
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1542 on 78 degrees of freedom
## Multiple R-squared: 0.9805, Adjusted R-squared: 0.9645
## F-statistic: 61.28 on 64 and 78 DF, p-value: < 2.2e-16#step <- stepAIC(model_1,direction = "both")
#summary(step)
#vif(step) untuk menentukan variabel yang akan dikurangiMenghapus variabel Fuel, System, MPFI
model_2 <-lm(formula = price ~ car_ID + fueltype + aspiration + enginelocation +
carwidth + carheight + curbweight + enginesize + boreratio +
stroke + compressionratio + peakrpm + citympg + carbodyhardtop +
carbodyhatchback + carbodysedan + carbodywagon + enginetypel +
enginetypeohcf + enginetypeohcv + enginetyperotor + cylindernumberfive +
cylindernumberthree + fuelsystem2bbl + companynameBMW +
companynameCHEVROLET + companynameDODGE + companynameHONDA +
companynameISUZU + companynameMAZDA + companynameMERCURY +
companynameMITSUBISHI + companynameNISSAN + companynamePLYMOUTH +
companynamePORSCHE + companynameRENAULT + companynameSAAB +
companynameTOYOTA + companynameVOLKSWAGEN + companynameVOLVO +
`symboling-1` + symboling0 + symboling1 + symboling2 + symboling3,
data = train)
step2 <- stepAIC(model_2,direction = "both")## Start: AIC=2118.93
## price ~ car_ID + fueltype + aspiration + enginelocation + carwidth +
## carheight + curbweight + enginesize + boreratio + stroke +
## compressionratio + peakrpm + citympg + carbodyhardtop + carbodyhatchback +
## carbodysedan + carbodywagon + enginetypel + enginetypeohcf +
## enginetypeohcv + enginetyperotor + cylindernumberfive + cylindernumberthree +
## fuelsystem2bbl + companynameBMW + companynameCHEVROLET +
## companynameDODGE + companynameHONDA + companynameISUZU +
## companynameMAZDA + companynameMERCURY + companynameMITSUBISHI +
## companynameNISSAN + companynamePLYMOUTH + companynamePORSCHE +
## companynameRENAULT + companynameSAAB + companynameTOYOTA +
## companynameVOLKSWAGEN + companynameVOLVO + `symboling-1` +
## symboling0 + symboling1 + symboling2 + symboling3
##
## Df Sum of Sq RSS AIC
## <none> 204720833 2118.9
## - symboling3 1 3783839 208504672 2119.6
## - stroke 1 4288290 209009122 2119.9
## - `symboling-1` 1 5490039 210210872 2120.7
## - carheight 1 5640068 210360901 2120.8
## - fuelsystem2bbl 1 6055432 210776264 2121.1
## - enginetypeohcv 1 6687636 211408468 2121.5
## - symboling2 1 6907444 211628276 2121.7
## - fueltype 1 8638298 213359131 2122.8
## - symboling0 1 9032729 213753562 2123.1
## - citympg 1 10023715 214744547 2123.8
## - symboling1 1 11490574 216211407 2124.7
## - compressionratio 1 12050667 216771499 2125.1
## - aspiration 1 13193728 217914561 2125.9
## - peakrpm 1 14896652 219617485 2127.0
## - cylindernumberfive 1 15934994 220655827 2127.7
## - carbodyhardtop 1 16699249 221420082 2128.1
## - boreratio 1 17155817 221876650 2128.4
## - companynamePORSCHE 1 19736609 224457441 2130.1
## - curbweight 1 20674401 225395234 2130.7
## - companynameCHEVROLET 1 22336176 227057009 2131.7
## - carbodyhatchback 1 32746549 237467381 2138.2
## - carbodysedan 1 34673500 239394333 2139.3
## - carbodywagon 1 41524173 246245006 2143.3
## - companynameBMW 1 41564228 246285060 2143.4
## - companynameISUZU 1 44077706 248798538 2144.8
## - carwidth 1 51150832 255871665 2148.8
## - companynameMERCURY 1 54504128 259224960 2150.7
## - enginesize 1 62111640 266832473 2154.8
## - companynameHONDA 1 63450033 268170866 2155.5
## - car_ID 1 64438608 269159441 2156.1
## - companynameSAAB 1 64613388 269334221 2156.2
## - companynameVOLVO 1 74868803 279589636 2161.5
## - companynameVOLKSWAGEN 1 75457322 280178155 2161.8
## - companynameDODGE 1 82010457 286731289 2165.1
## - companynameRENAULT 1 83038614 287759447 2165.6
## - enginetypeohcf 1 84939001 289659833 2166.6
## - cylindernumberthree 1 91875876 296596709 2169.9
## - companynameTOYOTA 1 95164070 299884902 2171.5
## - enginetyperotor 1 106382816 311103649 2176.8
## - companynameNISSAN 1 110528783 315249616 2178.7
## - companynamePLYMOUTH 1 111238939 315959772 2179.0
## - enginetypel 1 116350650 321071483 2181.3
## - enginelocation 1 122214869 326935701 2183.9
## - companynameMAZDA 1 129078970 333799803 2186.8
## - companynameMITSUBISHI 1 129730013 334450846 2187.1#summary(step2)
summary(model_2)##
## Call:
## lm(formula = price ~ car_ID + fueltype + aspiration + enginelocation +
## carwidth + carheight + curbweight + enginesize + boreratio +
## stroke + compressionratio + peakrpm + citympg + carbodyhardtop +
## carbodyhatchback + carbodysedan + carbodywagon + enginetypel +
## enginetypeohcf + enginetypeohcv + enginetyperotor + cylindernumberfive +
## cylindernumberthree + fuelsystem2bbl + companynameBMW + companynameCHEVROLET +
## companynameDODGE + companynameHONDA + companynameISUZU +
## companynameMAZDA + companynameMERCURY + companynameMITSUBISHI +
## companynameNISSAN + companynamePLYMOUTH + companynamePORSCHE +
## companynameRENAULT + companynameSAAB + companynameTOYOTA +
## companynameVOLKSWAGEN + companynameVOLVO + `symboling-1` +
## symboling0 + symboling1 + symboling2 + symboling3, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2459.5 -756.8 0.0 722.9 3535.9
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.667e+04 1.326e+04 -2.012 0.047002 *
## car_ID 1.146e+02 2.074e+01 5.526 2.76e-07 ***
## fueltype 1.129e+04 5.581e+03 2.023 0.045814 *
## aspiration -1.596e+03 6.385e+02 -2.500 0.014087 *
## enginelocation -2.894e+04 3.803e+03 -7.610 1.79e-11 ***
## carwidth 8.379e+02 1.702e+02 4.923 3.49e-06 ***
## carheight 1.811e+02 1.108e+02 1.635 0.105346
## curbweight 3.644e+00 1.164e+00 3.130 0.002311 **
## enginesize 7.203e+01 1.328e+01 5.425 4.26e-07 ***
## boreratio -2.919e+03 1.024e+03 -2.851 0.005323 **
## stroke -1.190e+03 8.346e+02 -1.425 0.157242
## compressionratio -9.442e+02 3.951e+02 -2.390 0.018804 *
## peakrpm 1.386e+00 5.217e-01 2.657 0.009226 **
## citympg 1.403e+02 6.439e+01 2.179 0.031730 *
## carbodyhardtop -2.807e+03 9.979e+02 -2.813 0.005944 **
## carbodyhatchback -3.468e+03 8.803e+02 -3.939 0.000154 ***
## carbodysedan -3.833e+03 9.456e+02 -4.053 0.000102 ***
## carbodywagon -4.682e+03 1.055e+03 -4.436 2.42e-05 ***
## enginetypel -1.679e+04 2.262e+03 -7.425 4.38e-11 ***
## enginetypeohcf -1.924e+04 3.033e+03 -6.344 7.14e-09 ***
## enginetypeohcv -1.617e+03 9.085e+02 -1.780 0.078193 .
## enginetyperotor 1.045e+04 1.471e+03 7.100 2.08e-10 ***
## cylindernumberfive -3.047e+03 1.109e+03 -2.748 0.007155 **
## cylindernumberthree 2.033e+04 3.082e+03 6.598 2.21e-09 ***
## fuelsystem2bbl 8.587e+02 5.070e+02 1.694 0.093501 .
## companynameBMW 4.772e+03 1.075e+03 4.438 2.40e-05 ***
## companynameCHEVROLET -6.077e+03 1.868e+03 -3.253 0.001571 **
## companynameDODGE -7.329e+03 1.176e+03 -6.234 1.18e-08 ***
## companynameHONDA -7.242e+03 1.321e+03 -5.483 3.32e-07 ***
## companynameISUZU -7.221e+03 1.580e+03 -4.570 1.44e-05 ***
## companynameMAZDA -1.116e+04 1.427e+03 -7.820 6.45e-12 ***
## companynameMERCURY -1.155e+04 2.273e+03 -5.082 1.82e-06 ***
## companynameMITSUBISHI -1.386e+04 1.767e+03 -7.840 5.86e-12 ***
## companynameNISSAN -1.436e+04 1.984e+03 -7.237 1.08e-10 ***
## companynamePLYMOUTH -1.815e+04 2.500e+03 -7.260 9.67e-11 ***
## companynamePORSCHE -7.995e+03 2.615e+03 -3.058 0.002880 **
## companynameRENAULT -1.847e+04 2.945e+03 -6.273 9.90e-09 ***
## companynameSAAB -1.613e+04 2.916e+03 -5.533 2.67e-07 ***
## companynameTOYOTA -2.194e+04 3.268e+03 -6.715 1.28e-09 ***
## companynameVOLKSWAGEN -2.349e+04 3.928e+03 -5.979 3.73e-08 ***
## companynameVOLVO -2.126e+04 3.569e+03 -5.956 4.14e-08 ***
## `symboling-1` 2.044e+03 1.267e+03 1.613 0.110027
## symboling0 3.072e+03 1.485e+03 2.069 0.041227 *
## symboling1 3.535e+03 1.515e+03 2.333 0.021696 *
## symboling2 2.757e+03 1.524e+03 1.809 0.073532 .
## symboling3 2.126e+03 1.588e+03 1.339 0.183710
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1453 on 97 degrees of freedom
## Multiple R-squared: 0.9785, Adjusted R-squared: 0.9685
## F-statistic: 97.98 on 45 and 97 DF, p-value: < 2.2e-16#vif(model_2)Menghapus beberapa variabel yang memiliki nilai p-value lebih dari 0.05 hingga mendapatkan model terbaik dengan nilai AIC terkecil
model_3 <- lm(formula = price ~ enginelocation +
carwidth + enginesize +
enginetyperotor + companynameBMW,
data = train)
summary(model_3)##
## Call:
## lm(formula = price ~ enginelocation + carwidth + enginesize +
## enginetyperotor + companynameBMW, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5574.0 -1768.7 35.4 1460.3 6817.3
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -69020.179 8883.196 -7.770 1.67e-12 ***
## enginelocation -16245.699 1687.905 -9.625 < 2e-16 ***
## carwidth 1280.438 151.935 8.428 4.31e-14 ***
## enginesize 104.741 8.115 12.907 < 2e-16 ***
## enginetyperotor 7171.787 1610.400 4.453 1.74e-05 ***
## companynameBMW 7348.186 1126.801 6.521 1.24e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2665 on 137 degrees of freedom
## Multiple R-squared: 0.8977, Adjusted R-squared: 0.894
## F-statistic: 240.5 on 5 and 137 DF, p-value: < 2.2e-16Melihat kesesuaian model
library(ResourceSelection)## Warning: package 'ResourceSelection' was built under R version 3.5.3## ResourceSelection 0.3-5 2019-07-22hoslem.test(train$price, fitted(model_3), g=10)##
## Hosmer and Lemeshow goodness of fit (GOF) test
##
## data: train$price, fitted(model_3)
## X-squared = -2.0765, df = 8, p-value = 1Prediksi harga
prediksi_harga <- predict(model_3, test[,-which(colnames(test)=='price')])
test$prediksi_harga <- prediksi_harga
head(test)## car_ID fueltype aspiration doornumber enginelocation wheelbase
## 4 4 0 1 1 1 99.8
## 5 5 0 1 1 1 99.4
## 6 6 0 1 0 1 99.8
## 16 16 0 1 1 1 103.5
## 17 17 0 1 0 1 103.5
## 20 20 0 1 0 1 94.5
## carlength carwidth carheight curbweight enginesize boreratio stroke
## 4 176.6 66.2 54.3 2337 109 3.19 3.40
## 5 176.6 66.4 54.3 2824 136 3.19 3.40
## 6 177.3 66.3 53.1 2507 136 3.19 3.40
## 16 189.0 66.9 55.7 3230 209 3.62 3.39
## 17 193.8 67.9 53.7 3380 209 3.62 3.39
## 20 155.9 63.6 52.0 1874 90 3.03 3.11
## compressionratio horsepower peakrpm citympg highwaympg price
## 4 10.0 102 5500 24 30 13950
## 5 8.0 115 5500 18 22 17450
## 6 8.5 110 5500 19 25 15250
## 16 8.0 182 5400 16 22 30760
## 17 8.0 182 5400 16 22 41315
## 20 9.6 70 5400 38 43 6295
## drivewheelfwd drivewheelrwd carbodyhardtop carbodyhatchback
## 4 1 0 0 0
## 5 0 0 0 0
## 6 1 0 0 0
## 16 0 1 0 0
## 17 0 1 0 0
## 20 1 0 0 1
## carbodysedan carbodywagon enginetypedohcv enginetypel enginetypeohc
## 4 1 0 0 0 1
## 5 1 0 0 0 1
## 6 1 0 0 0 1
## 16 1 0 0 0 1
## 17 1 0 0 0 1
## 20 0 0 0 0 1
## enginetypeohcf enginetypeohcv enginetyperotor cylindernumberfive
## 4 0 0 0 0
## 5 0 0 0 1
## 6 0 0 0 1
## 16 0 0 0 0
## 17 0 0 0 0
## 20 0 0 0 0
## cylindernumberfour cylindernumbersix cylindernumberthree
## 4 1 0 0
## 5 0 0 0
## 6 0 0 0
## 16 0 1 0
## 17 0 1 0
## 20 1 0 0
## cylindernumbertwelve cylindernumbertwo fuelsystem2bbl fuelsystem4bbl
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## 20 0 0 1 0
## fuelsystemidi fuelsystemmfi fuelsystemmpfi fuelsystemspdi
## 4 0 0 1 0
## 5 0 0 1 0
## 6 0 0 1 0
## 16 0 0 1 0
## 17 0 0 1 0
## 20 0 0 0 0
## fuelsystemspfi companynameAUDI companynameBMW companynameBUICK
## 4 0 1 0 0
## 5 0 1 0 0
## 6 0 1 0 0
## 16 0 0 1 0
## 17 0 0 1 0
## 20 0 0 0 0
## companynameCHEVROLET companynameDODGE companynameHONDA companynameISUZU
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 16 0 0 0 0
## 17 0 0 0 0
## 20 1 0 0 0
## companynameJAGUAR companynameMAZDA companynameMERCURY
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## 16 0 0 0
## 17 0 0 0
## 20 0 0 0
## companynameMITSUBISHI companynameNISSAN companynamePEUGEOT
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## 16 0 0 0
## 17 0 0 0
## 20 0 0 0
## companynamePLYMOUTH companynamePORSCHE companynameRENAULT
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## 16 0 0 0
## 17 0 0 0
## 20 0 0 0
## companynameSAAB companynameSUBARU companynameTOYOTA
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## 16 0 0 0
## 17 0 0 0
## 20 0 0 0
## companynameVOLKSWAGEN companynameVOLVO symboling-1 symboling0
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 0
## 16 0 0 0 1
## 17 0 0 0 1
## 20 0 0 0 0
## symboling1 symboling2 symboling3 prediksi_harga
## 4 0 1 0 10915.855
## 5 0 1 0 13999.945
## 6 0 1 0 13871.901
## 16 0 0 0 29634.431
## 17 0 0 0 30914.869
## 20 1 0 0 5596.641Melihat korelasi hasil prediksi dengan data asli
r <- cor(test$price,test$prediksi_harga)
r # 0.9456267## [1] 0.9456267Melihat nilai MAPE
library(forecast)## Warning: package 'forecast' was built under R version 3.5.3accuracy(prediksi_harga,test$price)## ME RMSE MAE MPE MAPE
## Test set 644.5205 2612.701 1953.348 1.884702 15.65352Kesimpulan Dari hasil analisis dari model regresi linier berganda memiliki nilai eror MAPE sebesar 15,6% yang memiliki kriteia BAIK dan untuk korelasi dari data asli dengan dengan hasil prediksi pada data testing sebesar 0.9456267.